Convert the equation d°y dy -1 xp dx and initial conditions y(0)= 1.14922, y'(0)= 1.0259 and y"(0)=-0.17941, into three first order -3-x-y 0 differential equations. Find the formulas for solving this system of equations by:- 1. Euler's forward difference method 2. The second order Runge-Kutta method based on k, =h f(x,»Yn) Ky = h f(Xn+h/2,Yn +k;/2) Yn+1=Yn+ Kz Find the numerical solution y at x=0.1, x= 0.2 and x= 0.3 by both methods using a step length h=0.1. Give your answers to 5 decimal places (no more and no less) however you should do you calculations with sufficient accuracy to ensure you answers are accurate to 5 decimal places. For the Euler method: Yo 1.14922 Y2= For the Runge-Kutta method: Yo 1.14922 %3D

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.